Artifacts in Render which actually don't exists geometrically
This could come from having to little geometry on your plane.
Basically Blender shows you editable points which we consider geo but uses triangles to compute the mesh. (not the most accurate description but oh well...)
Your boolean creates very long triangles which aren't displayed in the viewport but create problems in the render.
To fix this you can just subdivide the plane a bunch of times before applying the boolean.
Hope this helps :)